War is one of the four Horsemen of the Apocalypse, a boss which can be encountered at the end of the first floor in The Depths or Necropolis instead of a traditional boss once the player has beaten the game for the first time (killed Mom).
War appears as a red, humanoid-like being in a state of permanent rage with a pair of large, beady eyes riding on a stick horse. Unlike the other horsemen, War's stick horse appears to be a bull instead of a horse.

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While riding on his horse, he charges to the left or right and comes out on the other side, but does not stop until he has done 3 passthroughs. While charging, he will always enter the screen about 1/2 of the room height below where he left. If this distance would put him below the edge of the room, then he will come back in at the top of the room instead.

Also, while mounted, he shoots out an 8 directional shot, generally right after charging.

And also while riding, he will jump off and summon 5 Troll Bombs (similar to "The Tower" tarot card and "Anarchist Cookbook" item), wait for them to explode, and then land.

Activated when he reaches 50% of his total Health. Here, he will have lost his horse and will follow the player with extremely fast speed, similar to Lust or Gemini. However, like Gemini, he will occasionally pause to catch his breath, making a "splits" pose like the one Loki uses when firing bullets. He does this after you deal enough damage to him. Edmund also mentioned that he will slow down if you continue to attack him. It makes the fight easier for playthroughs with no speed upgrades.

If the player has the ability to fly, rocks will not protect him from War's phase 2, as he will climb those rocks in order to attack the player.

During phase 1, he leaves a Troll Bomb behind his path whenever he charges through the screen, and he will more frequently charge than regular War. He jumps off less often, but when he does, he summons 2 Mega Troll Bombs instead of half a dozen normal Troll Bombs.

During Phase 2, he normally chases you around the room, but when he is stunned, he fires out 6 bullets in six different directions. The champion War is also slower if the player continues to attack him.

He sometimes disappears from the screen completely after a jump attack. If you aren't able to exit your current room or kill him through AoE (e.g. Necronomicon), your game will be lost. In this case, homing tears will go towards you (confirmed only in a Famine-War combinate room in The Chest).

Using poison damage such as Bob's Rotten Head on War can cause glitches. If War takes damage while offscreen dropping bombs, he can get stuck and never return. This often requires you to restart the game. This also happens with The Candle. It's still possible to continue the game if you have either a teleporting item or the 1-Up / Ankh (Kill yourself with bombs, then respawn before the Boss Room). You can also still kill him with the Candle if you have it, as the Candle will damage him regardless of if he's on-screen or not, like it does for Mom's Heart/It Lives and Mom's doors.

During phase 1, it is possible that when War lands he will be invisible and stay invisible for the rest of the fight.

If you use the Book of Belial (and possibly other similar items or Tarot Cards) while War teleports off screen to summon troll bombs, he may become an invisible target, and will not spawn any troll bombs. Upon reaching half of his life bar, he will start chasing you as usual, but still remain invisible. (Confirmed)

If his horse is killed while he is spawning the Troll Bombs (like from poison), he will not return on screen. Killing his horse while he is still on your screen will result in War staying on your screen, doing no damage nor taking damage (he can still be damaged using The Candle).

If the player can fly and he flies over rocks, War can glitch out and go through the rocks and damage the player.

On rare occasions, usually after using the Book of Revelation on the Depths or Necropolis, War can be replaced by Conquest, despite that the versus screen tells you that War is the boss whom you're about to fight. Plus, after defeating him you don't get his White Pony but War's cube of meat.

If War is over rocks and the horse is killed (using Spectral Tears or anything like that) and still being shot at, War will be stuck in the rocks and cannot chase the player. This can be fixed with bombs.